A method and system are provided for the shaping and polishing of the surface of a material selected from the group consisting of electrically semi-conductive materials and conductive materials. An electrically non-conductive polishing lap incorporates a conductive electrode such that, when the polishing lap is placed on the material's surface, the electrode is placed in spaced-apart juxtaposition with respect to the material's surface. A liquid electrolyte is disposed between the material's surface and the electrode. The electrolyte has an electrochemical stability constant such that cathodic material deposition on the electrode is not supported when a current flows through the electrode, the electrolyte and the material. As the polishing lap and the material surface experience relative movement, current flows through the electrode based on (i) adherence to Faraday's Law, and (ii) a pre-processing profile of the surface and a desired post-processing profile of the surface.